Group memberships are normally controlled by your phone's Contacts app.
The options here are probably pretty limited.
If your contacts are synced to your Google Account:
Using a web browser, you can go to your GMail account, click the apps icon > more > contacts
Select the "label" for a group
Export the group as a CSV file
Very carefully edit the CSV file in a TEXT editor or spreadsheet
Import the CSV file.
Changing the group name should be simple enough, depending on how comfortable you are with this process.